Data-Discriminants of Likelihood Equations

Maximum likelihood estimation (MLE) is a fundamental computational problem in statistics. The problem is to maximize the likelihood function with respect to given data on a statistical model. An algebraic approach to this problem is to solve a very structured parameterized polynomial system called likelihood equations. For general choices of data, the number of complex solutions to the likelihood equations is finite and called the ML-degree of the model. The only solutions to the likelihood equations that are statistically meaningful are the real/positive solutions. However, the number of real/positive solutions is not characterized by the ML-degree. We use discriminants to classify data according to the number of real/positive solutions of the likelihood equations. We call these discriminants data-discriminants (DD). We develop a probabilistic algorithm for computing DDs. Experimental results show that, for the benchmarks we have tried, the probabilistic algorithm is more efficient than the standard elimination algorithm. Based on the computational results, we discuss the real root classification problem for the 3 by 3 symmetric matrix~model.Comment: 2 table

Three-point correlators for giant magnons

Three-point correlation functions in the strong-coupling regime of the AdS/CFT correspondence can be analyzed within a semiclassical approximation when two of the vertex operators correspond to heavy string states having large quantum numbers while the third vertex corresponds to a light state with fixed charges. We consider the case where the heavy string states are chosen to be giant magnon solitons with either a single or two different angular momenta, for various different choices of light string states.Comment: 15 pages. Latex. v2: Misprints corrected. Published versio

Correlators of Vertex Operators for Circular Strings with Winding Numbers in AdS5xS5

We compute semiclassically the two-point correlator of the marginal vertex operators describing the rigid circular spinning string state with one large spin and one windining number in AdS_5 and three large spins and three winding numbers in S^5. The marginality condition and the conformal invariant expression for the two-point correlator obtained by using an appropriate vertex operator are shown to be associated with the diagonal and off-diagonal Virasoro constraints respectively. We evaluate semiclassically the three-point correlator of two heavy circular string vertex operators and one zero-momentum dilaton vertex operator and discuss its relation with the derivative of the dimension of the heavy circular string state with respect to the string tension.Comment: 16 pages, LaTeX, no figure

A theory for the impact of a wave breaking onto a permeable barrier with jet generation

We model a water wave impact onto a porous breakwater. The breakwater surface is modelled as a thin barrier composed of solid matter pierced by channels through which water can flow freely. The water in the wave is modelled as a finite-length volume of inviscid, incompressible fluid in quasi-one-dimensional flow during its impact and flow through a typical hole in the barrier. The fluid volume moves at normal incidence to the barrier. After the initial impact the wave water starts to slow down as it passes through holes in the barrier. Each hole is the source of a free jet along whose length the fluid velocity and width vary in such a way as to conserve volume and momentum at zero pressure. We find there are two types of flow, depending on the porosity, ß , of the barrier. If ß : 0 = ß < 0.5774 then the barrier is a strong impediment to the flow, in that the fluid velocity tends to zero as time tends to infinity. But if ß : 0.5774 = ß = 1 then the barrier only temporarily holds up the flow, and the decelerating wave water passes through in a finite time. We report results for the velocity and impact pressure due to the incident wave water, and for the evolving shape of the jet, with examples from both types of impact. We account for the impulse on the barrier and the conserved kinetic energy of the flow. Consideration of small ß gives insight into the sudden changes in flow and the high pressures that occur when a wave impacts a nearly impermeable seawall

More three-point correlators of giant magnons with finite size

In the framework of the semiclassical approach, we compute the normalized structure constants in three-point correlation functions, when two of the vertex operators correspond to heavy string states, while the third vertex corresponds to a light state. This is done for the case when the heavy string states are finite-size giant magnons with one or two angular momenta, and for two different choices of the light state, corresponding to dilaton operator and primary scalar operator. The relevant operators in the dual gauge theory are Tr(F_{\mu\nu}^2 Z^j+...) and Tr(Z^j). We first consider the case of AdS_5 x S^5 and N = 4 super Yang-Mills. Then we extend the obtained results to the gamma-deformed AdS_5 x S^5_\gamma, dual to N = 1 super Yang-Mills theory, arising as an exactly marginal deformation of N = 4 super Yang-Mills.Comment: 14 pages, no figure

Control of hyperphosphatemia in regular hemodialysis (HDx) patients by calcium acetate (CA) versus calcium carbonate (CC). A double blind crossover prospective study

This study included fourty chronic renal failure patients aged 37-83 years (mean 51.3±7) on thrice weekly HDx for 4-144 month (Kt/V &gt;1.2). Acetate dialysate with calcium concentration of 3 mEq/L was used. All phosphate binders were discontinued for one month. Patients were divided in two groups. Group I (20 cases) received CA, while group II (20 cases) received CC in equimolar dose (10 mmol, of either t.i.d.) for one month. Crossover of treatment was done for another month while keeping patients on the same diet.Serum levels of total calcium (Ca), ionized Ca (iCa), phosphorus (P), alkaline phosphates (AP), urea (U), creatinine (Cr), ALT, AST, total proteins (TP) and albumin (Alb) were estimated before, and at the end of each month of CA and CC treatment. Serum Ca and iCa were significantly lower in group I after CA compared to values after CC (p&lt;0.01). Similar results in Ca levels were observed in group II (P&lt;0.05). In group II only serurn P was significantly lower after CA compared to its values after CC (P&lt;0.05). There was no significant difference in AP, U, Cr, ALT, AST, TP and Alb before, and at the end of each month of CA and CC treatment (P&gt;0.05 in all). We excluded 12.5% of cases due to CA intolerance while non of cases had similar intolerance to CC.Conclusion: 1) CA is not very superior to CC in control of hyperphosphataemia. 2) CA can be safely increased without the risk of hypercalcemia. 3) Active Vitamin D and high dialysate Ca can be used to suppress parathyroid activity more safely with CA than with CC. 4) Tolerability to CC is superior

Knowledge, attitudes and practices of prevention of mother to child transmision of HIV among women in Laroo Division Gulu Municipality, Uganda

This study is exploring the knowledge, attitudes and practices of Prevention of Mother to Child Transmission (PMTCT) of Human Immunodeficiency Virus (HIV) among child bearing women aged between 15- 45 years old in Laroo division in Gulu municipality. The goal of the study was to determine the level of attitude as well as of knowledge and belief about PMTCT and proportion of women practicing it among the child bearing women of Laroo Division. The Cross-sectional and Descriptive study design was applied in multistage sampling method with random selection of a parish followed by random selection of a village within the parish from which a sample of homesteads was randomly selected. From each homesteads, a single respondent was randomly selected and registered in the study. Questionnaires were given to respondents that had consented to take part in the study. A total of 208 respondents were registered and interviewed in a period of February to march 2011. There were 165 (79.3%) of the mothers who had knowledge about various PMTCT methods. Of these 86(52%) heard about PMTCT first from hospital. 50 (30%) knew about exclusive breast feeding, while another 50(30%) use of ART, 45(27%) knew about replacement feedings and only 21(13%) knew of elective caesarean section as method of PMTCT. However the majority of the mothers 159(96.5%) thought that PMTCT was beneficial. Nevertheless some mothers thought that PMTCT causes various counter indications including infertility 17 (10.5%) and abnormalities in children at birth 27 (16.7). Their HIV serostatus also varied. Of the 135(81.7%) screened for HIV 42(31.2%) tested HIV positive and only 27 (64.2%) used contraceptives to prevent pregnancy while they were HIV positive. However of the correspondents who tested positive in their last HIV tests, the majority (83%) had had at least a pregnancy after testing HIV positive of which 6.8% did not practice PMTCT. Our study suggests evidence that Knowledge, attitude and practice of PMTCT among women of reproductive age in Laroo Division in Gulu municipality in Northern Uganda is adequate.Nevertheless with the infection rate of 31.2% among them points out that there is a substantial burden of HIV in the women community

Un-oriented Quiver Theories for Majorana Neutrons

In the context of un-oriented open string theories, we identify quivers whereby a Majorana mass for the neutron is indirectly generated by exotic instantons. We discuss two classes of (Susy) Standard Model like quivers, depending on the embedding of SU(2)_W in the Chan-Paton group. In both cases, the main mechanism involves a vector-like pair mixing through a non-perturbative mass term. We also discuss possible relations between the phenomenology of Neutron-Antineutron oscillations and LHC physics in these models. In particular, a vector-like pair of color-triplet scalars or color-triplet fermions could be directly detected at LHC, compatibly with n-\bar{n} limits. Finally we briefly comment on Pati-Salam extensions of our models.Comment: More comments on phenomenology and fluxes, Re-discussion of SM-quivers compatible with n-cycles conditions Version accepted by JHE

Predicting hospital-onset Clostridium difficile using patient mobility data: A network approach

This is the final version. Available from Cambridge University Press via the DOI in this record. Objective: To examine the relationship between unit-wide Clostridium difficile infection (CDI) susceptibility and inpatient mobility and to create contagion centrality as a new predictive measure of CDI. Design: Retrospective cohort study. Methods: A mobility network was constructed using 2 years of patient electronic health record data for a 739-bed hospital (n = 72,636 admissions). Network centrality measures were calculated for each hospital unit (node) providing clinical context for each in terms of patient transfers between units (ie, edges). Daily unit-wide CDI susceptibility scores were calculated using logistic regression and were compared to network centrality measures to determine the relationship between unit CDI susceptibility and patient mobility. Results: Closeness centrality was a statistically significant measure associated with unit susceptibility (P< .05), highlighting the importance of incoming patient mobility in CDI prevention at the unit level. Contagion centrality (CC) was calculated using inpatient transfer rates, unit-wide susceptibility of CDI, and current hospital CDI infections. The contagion centrality measure was statistically significant (P< .05) with our outcome of hospital-onset CDI cases, and it captured the additional opportunities for transmission associated with inpatient transfers. We have used this analysis to create easily interpretable clinical tools showing this relationship as well as the risk of hospital-onset CDI in real time, and these tools can be implemented in hospital EHR systems Conclusions: Quantifying and visualizing the combination of inpatient transfers, unit-wide risk, and current infections help identify hospital units at risk of developing a CDI outbreak and, thus, provide clinicians and infection prevention staff with advanced warning and specific location data to inform prevention efforts.University of Rochester Clinical and Translational Science InstituteNational Institutes of HealthBurroughs Wellcome Fund Institutional Program Unifying Population and Laboratory Based Science

Multiregional Satellite Precipitation Products Evaluation over Complex Terrain

An extensive evaluation of nine global-scale high-resolution satellite-based rainfall (SBR) products is performed using a minimum of 6 years (within the period of 2000-13) of reference rainfall data derived from rain gauge networks in nine mountainous regions across the globe. The SBR products are compared to a recently released global reanalysis dataset from the European Centre for Medium-Range Weather Forecasts (ECMWF). The study areas include the eastern Italian Alps, the Swiss Alps, the western Black Sea of Turkey, the French Cévennes, the Peruvian Andes, the Colombian Andes, the Himalayas over Nepal, the Blue Nile in East Africa, Taiwan, and the U.S. Rocky Mountains. Evaluation is performed at annual, monthly, and daily time scales and 0.25° spatial resolution. The SBR datasets are based on the following retrieval algorithms: Tropical Rainfall Measuring Mission Multisatellite Precipitation Analysis (TMPA), the NOAA/Climate Prediction Center morphing technique (CMORPH), Precipitation Estimation from Remotely Sensed Information Using Artificial Neural Networks (PERSIANN), and Global Satellite Mapping of Precipitation (GSMaP). SBR products are categorized into those that include gauge adjustment versus unadjusted. Results show that performance of SBR is highly dependent on the rainfall variability. Many SBR products usually underestimate wet season and overestimate dry season precipitation. The performance of gauge adjustment to the SBR products varies by region and depends greatly on the representativeness of the rain gauge network